Math

QuestionIf (3x,y)=(1,4)(3^{x}, \sqrt{y})=(1,4), find x+yx+y. (a) 2 (b) 3 (c) 16 (d) 17

Studdy Solution

STEP 1

Assumptions1. The given equation is (3x,y)=(1,4)\left(3^{x}, \sqrt{y}\right)=(1,4). We need to find the value of x+yx+y

STEP 2

The given equation can be broken down into two separate equations. The first equation is x=1^{x}=1 and the second equation is y=4\sqrt{y}=4.

STEP 3

Let's solve the first equation 3x=13^{x}=1 for xx. Since any number raised to the power of0 is1, we can say that x=0x=0.

STEP 4

Now, let's solve the second equation y=4\sqrt{y}=4 for yy. Squaring both sides of the equation to eliminate the square root gives us y=42y=4^{2}.

STEP 5

Calculate the value of yy.
y=42=16y=4^{2}=16

STEP 6

Now that we have the values of xx and yy, we can find the value of x+yx+y.
x+y=0+16x+y=0+16

STEP 7

Calculate the value of x+yx+y.
x+y=0+16=16x+y=0+16=16So, x+y=16x+y=16.

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